If the function #f(x) = (3x-c)/(ax+2)# is a constant function, what is the value of #a*c# ?

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Answer 1 · 2016-07-12T09:21:51

#ac=-6#

#f(x)# being a constant function it will have same value for all real values of x.

So

#f(0) = f(1)#

#=>(3*0-c)/(a*0+2)=(3*1-c)/(a*1+2)#

#-c(a+2)=2*(3-c)#

#=>-ac-2c=6-2c#

#=>ac=-6#

Otherwise differentiating the function #f(x)# w.r.to x and equating #f'(x)=0# we can get the same result.